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Theorem :
Vertical angles are always equal in measure.

Proof : To prove m Ð AOC = m Ð BOD

m Ð AOC + m Ð COB = 1800 ( supplementary angles )

m Ð BOD + m Ð COB = 1800 ( supplementary angles )

i.e. m Ð AOC + m Ð COB = m Ð BOD + m Ð COB

or m Ð AOC = m Ð BOD.

Example 1

Measures of some angles are given below. Find the measures of their supplements.

a) 750     b) 1250    c) x0    d) (180 - x) 0    e) (90 + x) 0

Solution :

a) 1050

b) 550

c) (180 - x) 0

d) x0

e) (90 - x) 0

 

Index

Introduction

1.1 Points, Lines and Planes
1.2 Line Segment
1.3 Rays and Angles
1.4 Some Special Angles
1.5 Angles made by a Transversal
1.6 Transversal Across Two Parallel Lines
1.7 Conditions for Parallelism

Chapter 2

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